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November 2006 Remarks on zeta functions and K-theory over ${\mathbf F}_1$
Deitmar Anton
Proc. Japan Acad. Ser. A Math. Sci. 82(8): 141-146 (November 2006). DOI: 10.3792/pjaa.82.141


We show that the notion of zeta functions over the field of one element $\F_1$, as given in special cases by Soulé, extends naturally to all $\F_1$-schemes as defined by the author in an earlier paper. We further give two constructions of K-theory for affine schemes or $\F_1$-rings, we show that these coincide in the group case, but not in general.


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Deitmar Anton. "Remarks on zeta functions and K-theory over ${\mathbf F}_1$." Proc. Japan Acad. Ser. A Math. Sci. 82 (8) 141 - 146, November 2006.


Published: November 2006
First available in Project Euclid: 6 November 2006

zbMATH: 1173.14004
MathSciNet: MR2279281
Digital Object Identifier: 10.3792/pjaa.82.141

Primary: 11G25
Secondary: 11S40 , 11S70 , 14G15

Keywords: field of one element , zeta function

Rights: Copyright © 2006 The Japan Academy

Vol.82 • No. 8 • November 2006
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